document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=973893>Question 973893</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) What is the remainder when 2^31 is divided by 10?<BR>\n" );
document.write( "2) What is the remainder when 2^69 is divided by 5?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595922 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=595922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 raised to a power goes 2,4,8,6<BR>\n" );
document.write( "to the 9th power 512, then 1024, then 2048, 4096.<BR>\n" );
document.write( "Divide the exponent by 4 and see what is left over<BR>\n" );
document.write( "2^31 is 2^28 (which ends in 6).  The next three end in 2,4,and 8.  The remainder will be 8.\r<BR>\n" );
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document.write( "2^69 will have 17 repeats of the pattern and will end in 2 for 2^69.  The remainder will be 2, when divided by 5. </SPAN>\n" );
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